Mathematical Modelling of Droplet Evaporation
S. K. Wilson (Department of Mathematics, University of Strathclyde, Glasgow), G. J. Dunn (Department of Mathematics, University of Strathclyde, Glasgow), B. R. Duffy (Department of Mathematics, University of Strathclyde, Glasgow), S. David (School of Engineering and Electronics, University of Edinburgh, Edinburgh) and K. Sefiane (School of Engineering and Electronics, University of Edinburgh, Edinburgh)
The evaporation of a liquid droplet is a fundamental fluid mechanics problem arising in a wide variety of physical contexts ranging from the domestic to the industrial and the geophysical.
A mathematical model for the quasi-steady diffusion-limited evaporation of a pinned droplet which incorporates the dependence of the saturation concentration of vapour at the free surface of the droplet on temperature is formulated and solved both numerically and analytically in various physically realistic asymptotic limits.
The predictions of the model are found to be in good agreement with the results of recent physical experiments using variety of liquids and substrates.